The following disclosure relates to electrical circuits and signal processing.
A bandpass filter is a circuit that filters an input signal by significantly attenuating the input signal's frequency components that lie outside a passband while allowing the frequency components that lie within the passband to pass through with relatively less attenuation. Bandpass filter circuits can be characterized by parameters such as a center frequency (the frequency at which the passband of the filter is centered), a bandwidth (the frequency span of the filter passband), and a quality factor (a parameter relating to the ratio of the filter's center frequency to the filter's bandwidth, commonly referred to as the “Q” of the filter).
High quality-factor bandpass filters offer good frequency selectivity, allowing the filters to pass a relatively narrow band of frequencies while attenuating other frequencies. Conventional high quality-factor bandpass filters can be used in wireless transmitters to attenuate unwanted frequencies, such as harmonics of a desired signal, while passing a desired signal. Conventional high quality-factor bandpass filters can also be used in wireless receivers to attenuate unwanted signals (e.g., signals in an image band of the receiver) while passing a desired signal.
One way to implement a bandpass filter at radio frequencies is to use an LC tank circuit. A bandpass filter based on an LC tank circuit may exist in multiple forms. In one form, an inductor is connected in parallel with a capacitor. The filter transfer function in this case is the ratio between the output voltage across the parallel structure and an input current injected into the circuit. In another form, an inductor is connected in series with a capacitor. The filter transfer function in this case is the ratio between the output current flowing through the series structure and an input voltage applied across the circuit.
The center frequency (i.e., the frequency at which the transfer function reaches a local maximum) for a simple LC tank circuit is given by the equation 1/sqrt(LC), where L is the value of the inductor and C is the value of the capacitor. An LC tank circuit typically includes a resistance that affects the quality factor of the LC tank circuit. The resistance can be in the form of a physical resistor connected in parallel with a parallel LC structure, or can be in the form of a physical resistor connected in series with a series LC structure. The resistance can also be a result of loss in the inductor and/or in the capacitor.
When a bandpass filter is implemented monolithically in an integrated circuit, a tradeoff typically exists between the quality factor of the bandpass filter and the tolerance of the bandpass filter to process variations. Conventional CMOS process variations for metal-insulator-metal capacitors can cause variations in capacitance density on the order of ±20% due to factors such as varying dielectric thickness and permittivity. A ±20% variation in capacitance density translates to roughly a ±10% variation in center frequency for a conventional LC tank circuit. As the quality factor of an LC tank circuit increases, the passband of the LC tank circuit grows narrower, and a narrower range of frequency is passed unattenuated. Accordingly, a 10% deviation from the desired center frequency can result in an unacceptably large filter attenuation at the desired center frequency.
In order to compensate for process variations and increase process yields, the quality factor of a filter circuit (e.g., an LC tank circuit) can purposely be reduced to reduce the frequency selectivity of the filter circuit so that variations have less impact on the performance of the filter. This, however, sacrifices filter performance. Filter circuits can also be trimmed individually after processing to compensate for process variations, but individual adjustment increases the cost of manufacturing the filter circuit.